{
  "id": "1501.00763",
  "version": "v1",
  "published": "2015-01-05T05:16:16.000Z",
  "updated": "2015-01-05T05:16:16.000Z",
  "title": "On a lifting problem of L-packets",
  "authors": [
    "Bin Xu"
  ],
  "comment": "35 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G \\subseteq \\tilde{G}$ be two quasisplit connected reductive groups over a local field of characteristic zero and $G_{der} = \\tilde{G}_{der}$. Although the existence of L-packets is still conjectural in general, it is believed that the L-packets of $G$ should be the restriction of that of $\\tilde{G}$. Motivated by this, we hope to construct the L-packets of $\\tilde{G}$ from that of $G$. The primary example in our mind is when $G = Sp(2n)$, whose L-packets have been determined by Arthur (2013), and $\\tilde{G} = GSp(2n)$. As a first step, we need to consider some well-known conjectural properties of L-packets. In this paper, we show how they can be deduced from the conjectural endoscopy theory. As an application, we obtain some structural information about L-packets of $\\tilde{G}$ from that of $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-05T05:16:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lifting problem",
      "conjectural endoscopy theory",
      "well-known conjectural properties",
      "primary example",
      "local field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150100763X"
    }
  }
}